First off, I haven't seen big companies making this argument. Can you point us to a high quality source where one does?
Secondly, suppose the size of a market is X and BigCo has a 0.9X slice of it. Suppose the cost of complying with new regulation is 0.5X. Now it is impossible for anyone else to compete with BigCo, since there is no way for second place to be profitable in the market. However, BigCo is still worse off. Their revenues are now X, but their profits are now -0.4X compared to what they were before, since they gained 0.1X revenue and lost 0.5X in compliance costs.
So, if a BigCo were to make such an argument, that's at least one case where they could deploy it honestly while at the same time having their own best interests at heart.
Is it out of the goodness of their hearts that large companies complain about regulation hurting small businesses? Or is it because the regulation will cost them a ton of money they'd rather keep in the bank, and they know they already have enough market capture to continue to obliterate small businesses either way?
When someone says that regulations on large companies will actually hurt small businesses, the first thing you should do, is look who is claiming that, and see where they get their funding from. It's almost always a think tank funded by the biggest player in the market being discussed.